《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Direct observation and modelling of the crack–fibre interaction process in continuous fibre-reinforced ceramics：model experiments

MATERIAL E EGEERNG SEVIER Materials Science and Engineering A250(1998)285-290 Direct observation and modelling of the crack -fibre interaction process in continuous fibre-reinforced ceramics: model experiments Yutaka Kagawa*, Ken Got Institute of Industrial Science, The University of Tokyo, 7-22-1 Roppongi, Minato ku, Tokyo 106-8558, Japan Abstract The effect of the matrix-fibre interface bonding and debonding condition on the crack growth behaviour in a fibre-reinforced ceramic matrix composite was studied using a model glass fibre-reinforced PMMA matrix composite. The crack growth process rom a centre notch is monitored using a compression splitting test. From direct observation three characteristic stages can b identified in the crack growth process of the composite, namely elastic constraint(stage I), matrix crack bowing(stage In) and crack bridging(stage III). Partial interface debonding occurs at the end of stage I and cylindrical interface debonding occurs at the end of stage Il. The crack growth rate is accelerated just after the onset of interface partial debonding and this indicates that a debonded interface reduces the crack growth resistance. The partial interface debonding which occurs before fibre breaking plays an important role on the crack growth mechanism. C 1998 Elsevier Science S.A. All rights reserved Keywords: Crack deflection; Crack growth rate: Interface debonding 1. Introduction reported [9-13]. However, details of the 3D crack -fibre interaction processes have not yet been considered for Characteristic mechanical properties of fibre-rein- incorporation in the studies. Thus, it seems important forced ceramics arise from the development of a mi- to understand details of these stages of crack growth crofracture process. Recent experiments on a direct behaviour. In this paper, attention has been focused on observation of the fracture behaviour of continuous a detailed observation of crack-fibre interaction and its fibre-reinforced ceramic matrix composites revealed effect on the crack growth rate in continuous fibre-rein- that matrix cumulative microfracture occurs during the forced ceramic matrix composite, using a Sio, fibre-re- linear deformation range of the stress-strain curve. inforced PMMA model composite Evidence of matrix microcracking in Sic fibre-rein forced glass matrix composites was reported and theo retical considerations were also made [1-6]. The authors recently reported that the onset of early stage 2. Material and experimental procedure matrix cracking in the unidirectional Sic (NicalonTM) A commercially available pure Sio, fibre(diame- fibre-reinforced borosilicate glass composite occurs at ter =2.4 mm: 9R2, Toshiba Ceramics, Tokyo, Japan) an applied stress of x 90-100 MPa and that the exten sion of matrix microcracking was strongly related to was used as reinforcement and a commercially available matrix crack-fibre interactions [6-8]. The interaction PMMA plate(thickness=5.0 mm; ShinkoliteA, Mit process was divided into three stages, namely(i)elastic subishi Rayon, Tokyo, Japan) was used as matrix constraint,(1i) crack bowing and (iii) crack bridging Properties of the fibre and matrix are listed in Table 1 [9-11]. The effect of the elastic constraint and the [14, 15]. Two fibres aligned parallel to each other with spacing of a 2.0 mm were sandwiched between PMMA associated crack bowing on the fracture resistance of plates and subsequently hot-pressed in ambient air.The the unidirectional fibre-reinforced ceramics has been hot pressing temperature and pressure were 473 K and 2.5 MPa, respectively. Corresponding author. Tel. +81 3 34026231; fax: +81 3 The hot-pressed composite was mechanically cut into 34026350; e-mail: kagawa @iis. u-tokyo ac jp a double cleavage drilled compression(DCDC) speci- 0921-5093/98/S19.00 C 1998 Elsevier Science S.A. All rights reserved. PIS0921-5093098)00603·0

Materials Science and Engineering A250 (1998) 285–290 Direct observation and modelling of the crack–fibre interaction process in continuous fibre-reinforced ceramics: model experiments Yutaka Kagawa *, Ken Goto Institute of Industrial Science, The Uni6ersity of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan Abstract The effect of the matrix–fibre interface bonding and debonding condition on the crack growth behaviour in a fibre-reinforced ceramic matrix composite was studied using a model glass fibre-reinforced PMMA matrix composite. The crack growth process from a centre notch is monitored using a compression splitting test. From direct observation three characteristic stages can be identified in the crack growth process of the composite, namely elastic constraint (stage I), matrix crack bowing (stage II) and crack bridging (stage III). Partial interface debonding occurs at the end of stage I and cylindrical interface debonding occurs at the end of stage II. The crack growth rate is accelerated just after the onset of interface partial debonding and this indicates that a debonded interface reduces the crack growth resistance. The partial interface debonding which occurs before fibre breaking plays an important role on the crack growth mechanism. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Crack deflection; Crack growth rate; Interface debonding 1. Introduction Characteristic mechanical properties of fibre-rein￾forced ceramics arise from the development of a mi￾crofracture process. Recent experiments on a direct observation of the fracture behaviour of continuous fibre-reinforced ceramic matrix composites revealed that matrix cumulative microfracture occurs during the linear deformation range of the stress–strain curve. Evidence of matrix microcracking in SiC fibre-rein￾forced glass matrix composites was reported and theo￾retical considerations were also made [1–6]. The authors recently reported that the onset of early stage matrix cracking in the unidirectional SiC (Nicalon™) fibre-reinforced borosilicate glass composite occurs at an applied stress of :90–100 MPa and that the exten￾sion of matrix microcracking was strongly related to matrix crack–fibre interactions [6–8]. The interaction process was divided into three stages, namely (i) elastic constraint, (ii) crack bowing and (iii) crack bridging [9–11]. The effect of the elastic constraint and the associated crack bowing on the fracture resistance of the unidirectional fibre-reinforced ceramics has been reported [9–13]. However, details of the 3D crack–fibre interaction processes have not yet been considered for incorporation in the studies. Thus, it seems important to understand details of these stages of crack growth behaviour. In this paper, attention has been focused on a detailed observation of crack–fibre interaction and its effect on the crack growth rate in continuous fibre-rein￾forced ceramic matrix composite, using a SiO2 fibre-re￾inforced PMMA model composite. 2. Material and experimental procedure A commercially available pure SiO2 fibre (diame￾ter=2.4 mm; 9R2, Toshiba Ceramics, Tokyo, Japan) was used as reinforcement and a commercially available PMMA plate (thickness=5.0 mm; Shinkolite®A, Mit￾subishi Rayon, Tokyo, Japan) was used as matrix. Properties of the fibre and matrix are listed in Table 1 [14,15]. Two fibres aligned parallel to each other with spacing of :2.0 mm were sandwiched between PMMA plates and subsequently hot-pressed in ambient air. The hot pressing temperature and pressure were 473 K and 2.5 MPa, respectively. The hot-pressed composite was mechanically cut into a double cleavage drilled compression (DCDC) speci- * Corresponding author. Tel.: +81 3 34026231; fax: +81 3 34026350; e-mail: kagawa@iis.u-tokyo.ac.jp 0921-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S09 21- 5093(98)00603 - 0

Y. Kagawa, K Goto/ Materials Science and Engineering 4250(1998)285-290 Table I Properties of fibre and matrix Light Properties Sio, glass PMMA Strain Tensile strength(MPa) ≈70 Coefficient of thermal expansion (x CCD camera =6=1 Toshiba Ceramics, 9R2b Mitsubishi Rayon, Shinkolite* Fig. 2. Experimental set-up for direct observation. en[17]. Fig. I shows the shape and the dimensions of area was fixed to the specimen surface parallel to the the dCDC specimen. This specimen was chosen in fibre axis. The strain gage was mounted on the speci rder to have a slow matrix crack growth and to enable men surface at the crossing point of the fibre axis and direct observation of the crack front shape. All the the line 10 mm from the side end of the specimen.Ten surfaces of the specimen were mechanically ground and specimens were tested to obtain the common fracture polished to a 0 I um diamond paste finish. The nomina behaviour ibre volume fraction of the specimen was 0.02.A Fig. 2 shows the experimental set-up of the compres- hole(diameter 2r=8.0 mm) was drilled at the centre of sion splitting test. The crack growth behaviour during the DCDC specimen and natural pre-cracks were in- the test was directly observed from the direction per duced perpendicular to the fibre axis from the hole by pendicular to the crack plane by a CCD camera at bushing a sharp knife onto the edge of the hole. Fi- tached to a three-axes secure base. The crack front lly, two opposite-sided pre-cracks were carefully in erve duced in the DCDC specimen. The pre-crack lengths in light intensity [9]. The images from the CCD camera all the DCDC specimens were about 2 mm from the were stored in a video tape recorder at a rate of 30 hole edge. The ratio of the initial crack length from the images s. Some selected images during the compres- hole edge, co, to the hole radius, r, was co/r g 0.25, anc sion splitting test were picked up from the video record the distance between the initial crack tip to the fibre- ing to measure the total crack length, c. The definition matrix interface was x 4.0 mm. The DCDC specimen of the crack length used in this paper is shown in Fig of pure PMMA, hot-pressed under the same tempera- 3. The crack length, c, was defined as the length from he composite, was also prepare the hole edge to the crack front at the midsection of the for a comparison of the crack growth behaviour. The specimen through the thickness direction because the shape, dimensions and initial notch depth of the pure crack at the midsection of the specimen of pure PMMA PMMA specimen were completely identical to that of tended to grow faster than the crack at the surface the composite specimen A compression splitting test was performed at a defined as the crack front where it touches the interface constant crosshead speed of I mm min-I using ar The crack front curvature is also defined in Fig. 3: p Instron testing machine(Model 4204, Instron Corp, represents positive curvature,p represents negative USA)at 297 K in air. The specimen was sandwiched curvature, and when the crack front is straight p=oo between the rigid steel plates, and the load was applied perpendicular to the fibre axis. To measure the change of longitudinal strain near the fibre during the test, a 3. Results and discussion wire-wound strain gage with 2 x 5 mm- effective gage crosshead displacement relation of pure PMMA and dco points plotted 40 20 applied stress-crosshead displacement curve indicate ac the images selected to measure the crack length, c. Both near relation before the start growth from the pre-crack front. The stress for the Initial Crack Strain gage onset of non-linearity of the composite was larger than mm that of pure PMMa because of the reinforcing effect of Fig. 1. Shape and dimensions of the DCDC specimen the sio, fibre. After the onset of crack growth, the

286 Y. Kagawa, K. Goto / Materials Science and Engineering A250 (1998) 285–290 Table 1 Properties of fibre and matrix Properties PMMAb SiO2 glassa Young’s modulus (GPa) 70 3.3 Poisson’s ratio 0.14 0.3 Tensile strength (MPa) :70 :78 Coefficient of thermal expansion (× 0.5 60 10−6 K−1 ) a Toshiba Ceramics, c9R2b Mitsubishi Rayon, cShinkolite® Fig. 2. Experimental set-up for direct observation. men [17]. Fig. 1 shows the shape and the dimensions of the DCDC specimen. This specimen was chosen in order to have a slow matrix crack growth and to enable direct observation of the crack front shape. All the surfaces of the specimen were mechanically ground and polished to a 0.1 mm diamond paste finish. The nominal fibre volume fraction of the specimen was :0.02. A hole (diameter 2r=8.0 mm) was drilled at the centre of the DCDC specimen and natural pre-cracks were in￾duced perpendicular to the fibre axis from the hole by pushing a sharp knife onto the edge of the hole. Fi￾nally, two opposite-sided pre-cracks were carefully in￾duced in the DCDC specimen. The pre-crack lengths in all the DCDC specimens were about 2 mm from the hole edge. The ratio of the initial crack length from the hole edge, c0, to the hole radius, r, was c0/r:0.25, and the distance between the initial crack tip to the fibre– matrix interface was :4.0 mm. The DCDC specimen of pure PMMA, hot-pressed under the same tempera￾ture and pressure as the composite, was also prepared for a comparison of the crack growth behaviour. The shape, dimensions and initial notch depth of the pure PMMA specimen were completely identical to that of the composite specimen. A compression splitting test was performed at a constant crosshead speed of 1 mm min−1 using an Instron testing machine (Model 4204, Instron Corp., USA) at 297 K in air. The specimen was sandwiched between the rigid steel plates, and the load was applied perpendicular to the fibre axis. To measure the change of longitudinal strain near the fibre during the test, a wire-wound strain gage with 2×5 mm2 effective gage area was fixed to the specimen surface parallel to the fibre axis. The strain gage was mounted on the speci￾men surface at the crossing point of the fibre axis and the line 10 mm from the side end of the specimen. Ten specimens were tested to obtain the common fracture behaviour. Fig. 2 shows the experimental set-up of the compres￾sion splitting test. The crack growth behaviour during the test was directly observed from the direction per￾pendicular to the crack plane by a CCD camera at￾tached to a three-axes secure base. The crack front shape was easily observed by the change of reflected light intensity [9]. The images from the CCD camera were stored in a video tape recorder at a rate of 30 images s−1 . Some selected images during the compres￾sion splitting test were picked up from the video record￾ing to measure the total crack length, c. The definition of the crack length used in this paper is shown in Fig. 3. The crack length, c, was defined as the length from the hole edge to the crack front at the midsection of the specimen through the thickness direction because the crack at the midsection of the specimen of pure PMMA tended to grow faster than the crack at the surface. After the crack front reaches the fibre, the crack tip was defined as the crack front where it touches the interface. The crack front curvature is also defined in Fig. 3: r+ represents positive curvature, r− represents negative curvature, and when the crack front is straight r=. 3. Results and discussion 3.1. Crack growth beha6iour Fig. 4(a) and (b) show the typical applied stress– crosshead displacement relation of pure PMMA and the composite, respectively. The points plotted in the applied stress–crosshead displacement curve indicate the images selected to measure the crack length, c. Both curves show a linear relation before the start of crack growth from the pre-crack front. The stress for the onset of non-linearity of the composite was larger than that of pure PMMA because of the reinforcing effect of Fig. 1. Shape and dimensions of the DCDC specimen. the SiO2 fibre. After the onset of crack growth, the

y Kagawa K aterials Science and Engineering 4250(1998)285-290 Crack growth direction Crack Front Crack length Crack front Curvature radius Fig 3. Schematic drawing of the definition of the crack length. c, and crack curvature, p. curves of both pure PMMA and the composite showed from the hole edge perpendicular to the main crack in a non-linear deformation up to the total fracture of the both the pure PMMa and the composite specimens. specimen Then the crack proceeded rapidly and the specimen was Fig 5(a) and(b)show the fracture appearance of the completely separated into two pieces. Note that multi pure PMMA and the composite, respectively. Under ple fibre fracture was observed(Fig. 5(b)) because of loading, the cracks in pure PMMA and the PMMA he smaller fracture strain of the sio, fibre than that of matrix of the composite began to grow from the pre- the PMMA matrix crack tip and proceeded straight, and the crac A typical example of the crack growth process of the was parallel to the loading direction. After satu composite obtained by the direct observation is shown f the applied load(when the crosshead had in Fig. 6, and a schematic drawing of the crack growth over x 4 mm), the other, opposite-sided, crack initiated behaviour is shown in Fig. 7. The white dotted line in Fig 6 indicates the observed matrix crack front. Con idering the change of the crack front shape caused by interaction with the fibre, the crack growth process of the composite was divided into three characteristic stages, i.e., elastic constraint stage (stage I),matrix 000 crack bowing stage(stage II)and fibre bridging stage (stage IIl). At stage I, the crack front had positive curvature,pt, and the crack front shape was identical to that in pure PMMA. As the matrix crack front at the midsection of the specimen reached a l mm from the fibre, the crack decelerated only in front of the fibre Crosshead displacement /mm and the curvature became negative, i.e. p, Finally the crack front became a mixture of positive curvature, p+, and negative curvature, p The thermally induced stresses generated in the ma ix are tensile in the fibre axial direction, g? sive in the radial direction al and tensile in the circumference direction, a B. The thermal stresses in the matrix are estimated by following ref. [16 and the result is shown in Fig. 8. Note that in this reference a assumed to be constant with radial distance while the hermal stresses aT and al. decrease with the inverse of the square of the radial distance. The tensile stress in Crosshead displacement/mm the fibre axial direction accelerates the crack growth Fig. 4. Gross applied stress -crosshead displacement curve of both [12], and thus, thermal stress cannot be the reason for pure PMMA (a) and the composite(b) the observed crack deceleration The deceleration of the

Y. Kagawa, K. Goto / Materials Science and Engineering A250 (1998) 285–290 287 Fig. 3. Schematic drawing of the definition of the crack length, c, and crack curvature, r. curves of both pure PMMA and the composite showed a non-linear deformation up to the total fracture of the specimen. Fig. 5(a) and (b) show the fracture appearance of the pure PMMA and the composite, respectively. Under loading, the cracks in pure PMMA and the PMMA matrix of the composite began to grow from the pre￾crack tip and proceeded straight, and the crack plane was parallel to the loading direction. After saturation of the applied load (when the crosshead had moved over :4 mm), the other, opposite-sided, crack initiated from the hole edge perpendicular to the main crack in both the pure PMMA and the composite specimens. Then the crack proceeded rapidly and the specimen was completely separated into two pieces. Note that multi￾ple fibre fracture was observed (Fig. 5(b)) because of the smaller fracture strain of the SiO2 fibre than that of the PMMA matrix. A typical example of the crack growth process of the composite obtained by the direct observation is shown in Fig. 6, and a schematic drawing of the crack growth behaviour is shown in Fig. 7. The white dotted line in Fig. 6 indicates the observed matrix crack front. Con￾sidering the change of the crack front shape caused by interaction with the fibre, the crack growth process of the composite was divided into three characteristic stages, i.e., elastic constraint stage (stage I), matrix crack bowing stage (stage II) and fibre bridging stage (stage III). At stage I, the crack front had positive curvature, r+, and the crack front shape was identical to that in pure PMMA. As the matrix crack front at the midsection of the specimen reached :1 mm from the fibre, the crack decelerated only in front of the fibre and the curvature became negative, i.e. r−,. Finally, the crack front became a mixture of positive curvature, r+, and negative curvature, r−. The thermally induced stresses generated in the ma￾trix are tensile in the fibre axial direction, sz T, compres￾sive in the radial direction, sr T, and tensile in the circumference direction, su T. The thermal stresses in the matrix are estimated by following ref. [16] and the result is shown in Fig. 8. Note that in this reference sz T is assumed to be constant with radial distance while the thermal stresses sr T and su T, decrease with the inverse of the square of the radial distance. The tensile stress in the fibre axial direction accelerates the crack growth [12], and thus, thermal stress cannot be the reason for the observed crack deceleration. The deceleration of the Fig. 4. Gross applied stress–crosshead displacement curve of both pure PMMA (a) and the composite (b)

Y. Kagawa, K Goto/ Materials Science and Engineering 4250(1998)285-290 becomes unstable after interface partial debonding During stage I, as explained before, multiple fibre frac ture occurred perpendicular to the axis at intervals of At stage Il, the interface debonding area along the fibre circumference surface increased(Fig. 7), the crack proceeded with its negative front shape again because the matrix crack was directly trapped by the fibre. Just after the cylindrical interface debonding was formed around the fibre, the crack front entirely passed the fibre, the crack bridging process operated(stage Ill) and the crack front shape gradually became straight, P=00. These crack growth processes are very similar to those in SiC (SCS-6) fibre-reinforced PMMa ob. 20 mm served under cyclic loading [9], and SiC(SCS-6) fibre- reinforced glass matrix composite in a static fracture test [10,11] 3. 2. Fracture resistance The relationships between applied stress and crack length, c, for the composite and pure PMMA are shown in Fig 9. The change in strain with crack growth is also shown in Fig. 10. The fibre position is also indicated in these figures. The applied stress-crack length relation and strain-crack length relation of the composite were divided into three stages, which corre- pond to the stages defined by the direct observation 20 mm At stage I, the stress and the strain of the composite were higher than that of pure PMMA. This fact sug Fig. 5. Typical examples of fracture appearance of pure PMMA (a) gests that the composite specimen requires a larger and composite(b). applied stress for crack growth than the pure PMMA crack is an elastic constraint effect generated by the stiff At stage Il, the changes in the applied stress and the fibre [7,9], as demonstrated in layered composite mate- strain of the composite and of the pure PMMA were rials [ 8] almost the same and stress and strain increased with With further loading, the crack front continued to increasing crack length. After the crack front passed the bow with negative curvature, p, until partial interface fibre, the applied stress of the composite became 2-3 debonding occurred in front of the crack tip, and this MPa smaller than that of the pure PMMA. On the other hand, the strain of the composite increased to behaviour was observed when the crack front reached about two times that of pure PMMA. These results r0.2 mm from the interface. As interface debonding occurred ahead of the crack tip, it is of a tensile arise from the multiple fracture of the fibre at stage L, and tensile thermal stress in the axial direction because debonding type, caused by the interface tensile stress of fibre fracture the direct crack bowing and the fibre generated in front of the crack tip [7. 18). Just after the bridging mechanisms could not contribute to the tough- ening. While thermal stresses in the composite might be the midsection accelerated and the crack. where the released by interface debonding and sliding, they may curvature was forced to be negative by the elastic not entirely disappear. As mentioned before, the ther- mal stress generated in the matrix in the fibre axial reached the interface because the constraint effect il direction is tensile, and this stress helps crack growth creases with decreasing crack-fibre distance and disap- [12]. So, the stress of the composite was smaller than ears when interface debonding occurs [7-9]. Because that of pure PMMA at stages II and Ill. of the release of elastic constraint generated by the The applied plane-strain stress intensity factor, K fibre, the crack front at the midsection of the specimen of the DCDC specimen is obtained as

288 Y. Kagawa, K. Goto / Materials Science and Engineering A250 (1998) 285–290 Fig. 5. Typical examples of fracture appearance of pure PMMA (a) and composite (b). becomes unstable after interface partial debonding. During stage I, as explained before, multiple fibre frac￾ture occurred perpendicular to the axis at intervals of :3–5 mm. At stage II, the interface debonding area along the fibre circumference surface increased (Fig. 7), the crack proceeded with its negative front shape again because the matrix crack was directly trapped by the fibre. Just after the cylindrical interface debonding was formed around the fibre, the crack front entirely passed the fibre, the crack bridging process operated (stage III) and the crack front shape gradually became straight, r=. These crack growth processes are very similar to those in SiC (SCS-6) fibre-reinforced PMMA ob￾served under cyclic loading [9], and SiC (SCS-6) fibre￾reinforced glass matrix composite in a static fracture test [10,11]. 3.2. Fracture resistance The relationships between applied stress and crack length, c, for the composite and pure PMMA are shown in Fig. 9. The change in strain with crack growth is also shown in Fig. 10. The fibre position is also indicated in these figures. The applied stress–crack length relation and strain–crack length relation of the composite were divided into three stages, which corre￾spond to the stages defined by the direct observation. At stage I, the stress and the strain of the composite were higher than that of pure PMMA. This fact sug￾gests that the composite specimen requires a larger applied stress for crack growth than the pure PMMA specimen. At stage II, the changes in the applied stress and the strain of the composite and of the pure PMMA were almost the same and stress and strain increased with increasing crack length. After the crack front passed the fibre, the applied stress of the composite became 2–3 MPa smaller than that of the pure PMMA. On the other hand, the strain of the composite increased to about two times that of pure PMMA. These results arise from the multiple fracture of the fibre at stage I, and tensile thermal stress in the axial direction. Because of fibre fracture, the direct crack bowing and the fibre bridging mechanisms could not contribute to the tough￾ening. While thermal stresses in the composite might be released by interface debonding and sliding, they may not entirely disappear. As mentioned before, the ther￾mal stress generated in the matrix in the fibre axial direction is tensile, and this stress helps crack growth [12]. So, the stress of the composite was smaller than that of pure PMMA at stages II and III. The applied plane-strain stress intensity factor, K, of the DCDC specimen is obtained as crack is an elastic constraint effect generated by the stiff fibre [7,9], as demonstrated in layered composite mate￾rials [8]. With further loading, the crack front continued to bow with negative curvature, r−, until partial interface debonding occurred in front of the crack tip, and this behaviour was observed when the crack front reached :0.2 mm from the interface. As interface debonding occurred ahead of the crack tip, it is of a tensile debonding type, caused by the interface tensile stress generated in front of the crack tip [7,18]. Just after the partial interface debonding, the crack growth rate at the midsection accelerated and the crack, where the curvature was forced to be negative by the elastic constraint effect, proceeded until the crack front reached the interface, because the constraint effect in￾creases with decreasing crack–fibre distance and disap￾pears when interface debonding occurs [7–9]. Because of the release of elastic constraint generated by the fibre, the crack front at the midsection of the specimen

Y. Kagawa, K Goto/ Materials Science and Engineering 4250(1998)285-290 Static Crack growth Interface Debonding 2mm Crack Bowing Crack bridging 2mm 2mm Fig. 6. Crack growth process of the composite from direct observation. The white dotted-line indicates matrix crack front. fitting of the experimentally obtained F(c/r) for 0.5< r≤3.0 yields: where a is the applied stress, c is the crack length and the s) is the dimensionless shape factor. As F(c/r) for =1.0391-099331(c/r)+0. 27049(c/r)2 specimen used could not be obtained from the literature, it was obtained from the experiment of the +0.062984(c/r)3-0.041821(c/r)4 pure PMMA specimen, assuming that the applied in +0.0053704(c/r)3 tensity factor is equal to the critical stress intensity factor of pure PMMa ShinkoliteA, KcN The applied stress intensity of the composite, K, is 1.0 MPaym [8D). The fifth order polynomial curve obtained substituting Eq (2) into Eq (1).Fig11shows the change of the normalised K, i.e. K/Km with the nterface Circumference stress: o Crack Plane Crack Plane Stage II 020苏 2≈4MPa Radial stress: o StageⅢ 050010001500200025003000 Crack Plane CrackPlane Distance from interface /um 7. Schematic drawing of crack growth process of the composite ig. 8. Thermal stress distribution in the matrix and the fibre

Y. Kagawa, K. Goto / Materials Science and Engineering A250 (1998) 285–290 289 Fig. 6. Crack growth process of the composite from direct observation. The white dotted-line indicates matrix crack front. K=Fc r  sc 1 2 (1) where s is the applied stress, c is the crack length and F(c/r) is the dimensionless shape factor. As F(c/r) for the specimen used could not be obtained from the literature, it was obtained from the experiment of the pure PMMA specimen, assuming that the applied in￾tensity factor is equal to the critical stress intensity factor of pure PMMA (Shinkolite®A, Kc m: 1.0 MPa m [8]). The fifth order polynomial curve fitting of the experimentally obtained F(c/r) for 0.55 c/r53.0 yields: F(c/r) =1.0391−0.99331 (c/r)+0.27049 (c/r) 2 +0.062984 (c/r) 3−0.041821 (c/r) 4 +0.0053704 (c/r) 5 (2) The applied stress intensity of the composite, K, is obtained substituting Eq. (2) into Eq. (1). Fig. 11 shows the change of the normalised K, i.e. K/K m c with the Fig. 7. Schematic drawing of crack growth process of the composite. Fig. 8. Thermal stress distribution in the matrix and the fibre

Y. Kagawa, K Goto/ Materials Science and Engineering 4250(1998)285-290 Fiber Ill, K exhibits a slightly smaller value than the critical 9000 stress intensity factor of the matrix, K 显40 O PMMA The 3D crack-fibre interaction in the composite studied is divided into three stages: elastic constraint stage(stage D), matrix crack bowing stage(stage II)and Normalized crack length c/r crack bridging stage(stage mechanism for fracture resistance of the composite Fig.9. Applied stress versus crack length of pure PMMA and the within this experiment is the elastic constraint effect by Fiber The interface partial debonding phenomena decide he termination of the stages: the first partial debonding n front of the crack tip gives the end of stage I. The formation of the cylindrical debonding gives the end of stage II. To have an efficient toughening effect gener ated from the fibre. the fibre-matrix interface must bond until the crack reaches the fibre. on the other hand. after the crack reaches the fibre. the interface must debond before the crack penetrates into the fibr Normalized crack length, c/r Fig. 10. Strain gauge reading versus crack length of pure PMMA and the composite References Fiber [1 M.W. Barsoum, P. Kangutkar, A.S.D. Wang, Compos. Sci Technol.44(1992)257-269 2A.S.D. Wang, X.G. Huang, M.w. Barsoum, Compos. Sci. Tech nol.44(1992)271-282 BIRY. Kim, N.J. Pagano, J. Am. Ceram. Soc. 74(5)(1991) [4 N.J. Pagano, R.Y. Kim, Mech. Compos Mater. Struct. 1(1994) [R.E. Dutton, N.J. Pagano, R.Y. Kim, J. Am. Ceram Soc. 79(4) (1996)865-872 Normalized crack length, c/r [6 Y. Kagawa, K. Goto, Ceram. (1995)247-251 [ K. Goto, Y. Kagawa, Mater A176(1994)357-361 Fig. Il Normalised stress intensity factor, K/Kc, versus normalised 8K. Goto, Y. Kagawa, Ceram. (1995)253-258 crack length, c/r, of the composite and pure PMMA(K/Km=l) 9 K Goto, Y. Kagawa, K. Nojima, H. Iba, Mater. Sci. Eng. A212 0]K J. Jpn. Ceram. Soc. 100(1993)6 increase of the normalised crack length, c/r. At stage L, []Y Mater. Sci. Eng. A221(1996)163-172. K is 1.2 times as large as the value for pure [12] T M A.S. Argon, Mech. Mater. 19(1995)343- PMMA. This behaviour is explained by the elastic [3]AF58 M. Ortiz, J. Mech. Phys. Solids 39(6)(1991) constraint effect; i.e. that the stress at the crack tip is [14 Toshiba Ceramics Catalogue, 1995 reduced by the stiffer fibre, since Er< Em [7, 8]. As (15 Mitsubishi Rayon Catalogue, 1994 mentioned before, the applied stresses on the composite [16]H. Poritsky, Physics 5(12)(1934)406-411 at stages II and Ill with the same crack length were [17 C. Jansen, Specimen for fracture mechanics studies on glass. The maller than that of pure PMMA. After the crack front Ceramic Society of Japan, 10th Inter. Cong on Glass, Kyoto Japan, July, 1974 reached the fibre-matrix interface, i. e, in stages II and [18]J. Cook, J.E. Gordon, Proc. R Soc. A282(1964)508

290 Y. Kagawa, K. Goto / Materials Science and Engineering A250 (1998) 285–290 Fig. 9. Applied stress versus crack length of pure PMMA and the composite. Fig. 10. Strain gauge reading versus crack length of pure PMMA and the composite. Fig. 11. Normalised stress intensity factor, K/Kc m, versus normalised crack length, c/r, of the composite and pure PMMA (K/Kc m=1). III, K exhibits a slightly smaller value than the critical stress intensity factor of the matrix, Kc m. 4. Summary The 3D crack–fibre interaction in the composite studied is divided into three stages: elastic constraint stage (stage I), matrix crack bowing stage (stage II) and crack bridging stage (stage III). The most effective mechanism for fracture resistance of the composite within this experiment is the elastic constraint effect by a stiffer fibre. The interface partial debonding phenomena decide the termination of the stages: the first partial debonding in front of the crack tip gives the end of stage I. The formation of the cylindrical debonding gives the end of stage II. To have an efficient toughening effect gener￾ated from the fibre, the fibre–matrix interface must bond until the crack reaches the fibre. On the other hand, after the crack reaches the fibre, the interface must debond before the crack penetrates into the fibre. References [1] M.W. Barsoum, P. Kangutkar, A.S.D. Wang, Compos. Sci. Technol. 44 (1992) 257–269. [2] A.S.D. Wang, X.G. Huang, M.W. Barsoum, Compos. Sci. Tech￾nol. 44 (1992) 271–282. [3] R.Y. Kim, N.J. Pagano, J. Am. Ceram. Soc. 74 (5) (1991) 1082–1090. [4] N.J. Pagano, R.Y. Kim, Mech. Compos. Mater. Struct. 1 (1994) 3–29. [5] R.E. Dutton, N.J. Pagano, R.Y. Kim, J. Am. Ceram. Soc. 79 (4) (1996) 865–872. [6] Y. Kagawa, K. Goto, Ceram. Trans. 57 (1995) 247–251. [7] K. Goto, Y. Kagawa, Mater. Sci. Eng. A176 (1994) 357–361. [8] K. Goto, Y. Kagawa, Ceram. Trans. 57 (1995) 253–258. [9] K. Goto, Y. Kagawa, K. Nojima, H. Iba, Mater. Sci. Eng. A212 (1996) 69–74. [10] K. Sekine, Y. Kagawa, J. Jpn. Ceram. Soc. 100 (1993) 621–625. [11] Y. Kagawa, K. Sekine, Mater. Sci. Eng. A221 (1996) 163–172. [12] T.M. Mower, A.S. Argon, Mech. Mater. 19 (1995) 343–364. [13] A.F. Bower, M. Ortiz, J. Mech. Phys. Solids 39 (6) (1991) 815–858. [14] Toshiba Ceramics Catalogue, 1995. [15] Mitsubishi Rayon Catalogue, 1994. [16] H. Poritsky, Physics 5 (12) (1934) 406–411. [17] C. Jansen, Specimen for fracture mechanics studies on glass, The Ceramic Society of Japan, 10th Inter. Cong. on Glass, Kyoto, Japan, July, 1974. [18] J. Cook, J.E. Gordon, Proc. R. Soc. A282 (1964) 508. increase of the normalised crack length, c/r. At stage I, K is :1.2 times as large as the value for pure PMMA. This behaviour is explained by the elastic constraint effect; i.e. that the stress at the crack tip is reduced by the stiffer fibre, since EfEm [7,8]. As mentioned before, the applied stresses on the composite at stages II and III with the same crack length were smaller than that of pure PMMA. After the crack front reached the fibre–matrix interface, i.e., in stages II and